[PPT] - Feedback Control and Visual Servoing Lecture 11 What will you take PowerPoint Presentation

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Feedback Control and Visual Servoing

Lecture 11

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What will you take home today?

Introduction to Control Recap - PD Controllers PID Controllers Visual Servoing Different Formulations Interaction Matrix Control Law Case-Study: Learning-based approach

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Joint Space - PD Controller

Proportional – Derivative control law in joint space

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Joint Space Control

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Passive Natural Systems - Conservative

x

k

m

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Passive Natural Systems - Conservative

V kx = 1 2

2 x t

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Passive Natural System – Dissipative

x

k

m

x x x x Friction

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Passive Natural System – Dissipative

x

k

m

x x x x Friction

mx bx kx !! ! + + = 0

!! ! x b m x k m x + + = 0

x t

Oscillatory damped

x t

Critically damped

x t

Over damped

Natural frequency damping

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Critically Damped System – Choose B

m

n n

2 2 w w ×

mx bx kx !! ! + + = 0

!! ! x b m x k m x + + = 0

bm

m

n

2 2 w

w n

2

Natural damping ratio as a reference value

Critically damped when b/m=2wn

x w

n n

b m = 2 m b km = 2

Critically damped system: x n

b km = = 1 2 ( )

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1 DOF Robot Control

m

f

x0 xd

V(x)

x0 xd

x

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Asymptotic Stability – Converging to a value

m

f

x0 xd

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Test yourself

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Control Partitioning

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Non-Linearity

m

f

x0 xd System f

( , !) x x

+ +

ˆ m

f ¢

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Disturbance rejection

+

+
+

+

d

x

¢ kp

¢ kv

¢ f

System

f

fdist

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Steady-State Error The steady-state

!! ! e k e k e f m

v p dist

+ ¢ + ¢ =

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Example

m

f

fdist

kp

m

x x x x

kv

fdist

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PID controller

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Test yourself

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What will you take home today?

Introduction to Control Recap - PD Controllers PID Controllers Visual Servoing Different Formulations Interaction Matrix Control Law Case-Study: Learning-based approach

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Camera-Robot Configurations

Image from: CHANG, W., WU, C.. Hand-Eye Coordination for Robotic Assembly Tasks. International Journal of Automation and Smart Technology,

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Image-based visual servoing

Current Image Goal Image

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Camera Motion to Image Motion

vx vy vz ωz ωx ωy

Slides adapted from Peter Corke

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The Image Jacobian

ω v ˆ f = f ρ ( ˙ u, ˙ v)T (X, Y, Z)T

✓ ˙ u ˙ v ◆ = ✓ − ˆ f/Z u/Z uv/ ˆ f −( ˆ f + u2/ ˆ f) v − ˆ f/Z v/Z ˆ f + u2/ ˆ f −uv/ ˆ f −u ◆ B B B B B B @ vx vy vz ωx ωy ωz 1 C C C C C C A Slides adapted from Peter Corke

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Camera Motion to Image Motion

vx vy vz ωz ωx ωy

f = [u, v]T

˙ r = [vx, xy, vz, ωx, ωy, ωz]T

Slides adapted from Peter Corke

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Optical flow Patterns

Slides adapted from Peter Corke

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Image-based visual servoing

Getting a camera velocity to minimize the error between the current and goal image

Current Image Goal Image

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Image-based visual servoing

Current Image Goal Image

✓ ˙ u ˙ v ◆ = ✓ − ˆ f/Z u/Z uv/ ˆ f −( ˆ f + u2/ ˆ f) v − ˆ f/Z v/Z ˆ f + u2/ ˆ f −uv/ ˆ f −u ◆ B B B B B B @ vx vy vz ωx ωy ωz 1 C C C C C C A

J(u, v, Z)

Slides adapted from Peter Corke

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Image-based visual servoing

Current Image Goal Image

        ˙ u1 ˙ v1 ˙ u2 ˙ v2 ˙ u3 ˙ v3         =   J(u1, v1, Z1) J(u2, v2, Z2) J(u3, v3, Z3)           vx vy vz ωx ωy ωz        

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Image-based visual servoing

        ˙ u1 ˙ v1 ˙ u2 ˙ v2 ˙ u3 ˙ v3         =   J(u1, v1, Z1) J(u2, v2, Z2) J(u3, v3, Z3)           vx vy vz ωx ωy ωz        

        vx vy vz ωx ωy ωz         =   J(u1, v1, Z1) J(u2, v2, Z2) J(u3, v3, Z3)  

−1

        ˙ u1 ˙ v1 ˙ u2 ˙ v2 ˙ u3 ˙ v3        

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Desired Pixel Velocity

Slides adapted from Peter Corke

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Simulation

Slides adapted from Peter Corke

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Point Correspondences

How to find them? Features, Markers

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What will you take home today?

Introduction to Control Recap - PD Controllers PID Controllers Visual Servoing Different Formulations Interaction Matrix Control Law Case-Study: Learning-based approach

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Training Deep Neural Networks for Visual Servoing

Bateux et al. ICRA 2018

1.

Instead of using features, use the whole image to compare to given goal image

a. Challenge: Small convergence region due to non-linear cost function

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Training Deep Neural Networks for Visual Servoing

Bateux et al. ICRA 2018

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Training Deep Neural Networks for Visual Servoing

Bateux et al. ICRA 2018